BRECKENRIDGE, Colo. — On nights when she could not crash on a friend’s couch or unroll a sleeping mat on an attic floor, Chelsea Lilly tucked her silver Subaru into a supermarket parking lot or a dark spot along a mountain pass, wrapped herself in a green Army blanket and watched movies on her phone until she fell asleep.

Getting work at a day spa in this bustling ski town had been easy, but finding an affordable apartment this winter proved almost impossible. So Ms. Lilly, 34, bounced along an itinerant path of couches and borrowed bedrooms that has become a fact of life for workers in jewel-box tourist towns across the country. Nights in the Subaru got so cold that she shivered awake every few hours and ran the engine to thaw out.